Description 
xvi, 554 pages : illustrations ; 24 cm. 
Content Type 
text 
Format 
volume 
Series 
Graduate texts in mathematics, 00725285 ; 267 

Graduate texts in mathematics ; 267.

Bibliography 
Includes bibliographical references and index. 
Contents 
The experimental origins of quantum mechanics: Is light a wave or a particle? ; Is an electron a wave or a particle? ; Schrödinger and Heisenberg ; A matter of interpretation ; Exercises  A first approach to classical mechanics: Motion in R¹ ; Motion in R[superscript n] ; Systems of particles ; Angular momentum ; Poisson brackets and Hamiltonian mechanics ; The Kepler problem and the RungeLenz vector ; Exercises  First approach to quantum mechanics: Waves, particles, and probabilities ; A few words about operators and their adjoints ; Position and the position operator ; Momentum and the momentum operator ; The position and momentum operators ; Axioms of quantum mechanics : operators and measurements ; Timeevolution in quantum theory ; The Heisenberg picture ; Example : a particle in a box ; Quantum mechanics for a particle in R [superscript n] ; Systems of multiple particles ; Physics notation ; Exercises  The free Schrödinger equation: Solution by means of the Fourier transform ; Solution as a convolution ; Propagation of the wave packet : first approach ; Propagation of the wave packet : second approach ; Spread of the wave packet ; Exercises  Particle in a square well: The timeindependent Schrödinger equation ; Domain questions and the matching conditions ; Finding squareintegrable solutions ; Tunneling and the classically forbidden region ; Discrete and continuous spectrum ; Exercises  Perspectives on the spectral theorem: The difficulties with the infinitedimensional case ; The goals of spectral theory ; A guide to reading ; The position operator ; Multiplication operators ; The momentum operator  The spectral theorem for bounded selfadjoint operators : statements: Elementary properties of bounded operators ; Spectral theorem for bounded selfadjoint operators, I ; Spectral theorem for bounded selfadjoint operators, II ; Exercises  The spectral theorem for bounded selfadjoint operators : proofs: Proof of the spectral theorem, first version ; Proof of the spectral theorem, second version ; Exercises  Unbounded selfadjoint operators: Introduction ; Adjoint and closure of an unbounded operator ; Elementary properties of adjoints and closed operators ; The spectrum of an unbounded operator ; Conditions for selfadjointness and essential selfadjointness ; A counterexample ; An example ; The basic operators of quantum mechanics ; Sums of selfadjoint operators ; Another counterexample ; Exercises  The spectral theorem for unbounded selfadjoint operators: Statements of the spectral theorem ; Stone's theorem and oneparameter unitary groups ; The spectral theorem for bounded normal operators ; Proof of the spectral theorem for unbounded selfadjoint operators ; Exercises  The harmonic oscillator: The role of the harmonic oscillator ; The algebraic approach ; The analytic approach ; Domain conditions and completeness ; Exercises  The uncertainty principle: Uncertainty principle, first version ; A counterexample ; Uncertainty principle, second version ; Minimum uncertainty states ; Exercises  Quantization schemes for Euclidean space: Ordering ambiguities ; Some common quantization schemes ; The Weyl quantization for R²[superscript n] ; The "No go" theorem of Groenewold ; Exercises  The StoneVon Neumann theorem: A heuristic argument ; The exponentiated commutation relations ; The theorem ; The SegalBargmann space ; Exercises  The WKB approximation: Introduction ; The old quantum theory and the BohrSommerfeld condition ; Classical and semiclassical approximations ; The WKB approximation away from the turning points ; The Airy function and the connection formulas ; A rigorous error estimate ; Other approaches ; Exercises  Lie groups, Lie algebras, and representations: Summary ; Matrix Lie groups ; Lie algebras ; The matrix exponential ; The Lie algebra of a matrix Lie group ; Relationships between Lie groups and Lie algebras ; Finitedimensional representations of Lie groups and Lie algebras ; New representations from old ; Infinitedimensional unitary representations ; Exercises  Angular momentum and spin: The role of angular momentum in quantum mechanics ; The angular momentum operators in R³ ; Angular momentum from the Lie algebra point of view ; The irreducible representations of so(3) ; The irreducible representations of SO(3) ; Realizing the representations inside L²(S²)  Realizing the representations inside L²(M³) ; Spin ; Tensor products of representations : "addition of angular momentum" ; Vectors and vector operators ; Exercises  Radial potentials and the hydrogen atom: Radial potentials ; The hydrogen atom : preliminaries ; The bound states of the hydrogen atom ; The RungeLenz vector in the quantum Kepler problem ; The role of spin ; RungeLenz calculations ; Exercises  Systems and subsystems, multiple particles: Introduction ; Traceclass and HilbertSchmidt operators ; Density matrices : the general notion of the state of a quantum system ; Modified axioms for quantum mechanics ; Composite systems and the tensor product ; Multiple particles : bosons and fermions ; "Statistics" and the Pauli exclusion principle ; Exercises  The path integral formulation of quantum mechanics: Trotter product formula ; Formal derivation of the Feynman path integral ; The imaginarytime calculation ; The Wiener measure ; The FeynmanKac formula ; Path integrals in quantum field theory ; Exercises  Hamiltonian mechanics on manifolds: Calculus on manifolds ; Mechanics on symplectic manifolds ; Exercises  Geometric quantization on Euclidean space: Introduction ; Prequantization ; Problems with prequantization ; Quantization ; Quantization of observables ; Exercises  Geometric quantization on manifolds: Introduction ; Line bundles and connections ; Prequantization ; Polarizations ; Quantization without halfforms ; Quantization with halfforms : the real case ; Quantization with halfforms : the complex case ; Pairing maps ; Exercises  A review of basic material: Tensor products of vector spaces ; Measure theory ; Elementary functional analysis ; Hilbert spaces and operators on them. 
Subject 
Quantum theory  Mathematics.

ISBN 
9781461471158 (acidfree paper) 

146147115X (acidfree paper) 

9781461471165 (eBook) 

1461471168 (eBook) 
OCLC number 
828487961 
